The scheduling of Agile Earth Observation Satellites is to select a subset of candidate targets each associated with a profit during their visible time windows in order to maximize the collected profits, under some operational constraints. For each pair of two consecutive observations, a transition time is required to perform a rotating movement of the camera, depending on the start times of the two observations. This time-dependency significantly increases the complexity of the scheduling problem. To solve this problem efficiently, we model the time-dependent transition time and prove that it satisfies the First-In-First-Out rule and the triangle inequalities rule. On this basis, we develop a novel hybrid heuristic, called "Greedy Randomized Iterated Local Search" (GRILS). A specific insert operator including a fast feasibility check and an assignment procedure are specifically designed to address the operational constraints of the scheduling. Extensive experiments on the single satellite instances and multi-satellite instances demonstrate that our algorithm outperforms the state-of-the-art algorithms with respect to solution quality and computation time. Index Terms-time-dependent transition time, satellite scheduling, GRILS heuristic.